Finite Group Databasebeta

← #16831512

Subgroups — #16831512

Order 3712.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271851C211yesmaximal, characteristic, complemented
2#14271798C211yesmaximal, characteristic
3#14271485C211yesmaximal, characteristic, complemented
4#14271475C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271408C211yesmaximal, characteristic, complemented
7#14271391C211yesmaximal, characteristic, complemented
8#14271360C211yesmaximal, characteristic, complemented
9#14271315C211yesmaximal, characteristic, complemented
10#14271315C211yesmaximal, characteristic, complemented
11#14271265C211yesmaximal, characteristic, complemented
12#14271236C211yesmaximal, characteristic, complemented
13#14271166C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#490C211yesmaximal, characteristic, complemented
16C2×D4×D29—21no—
17C2×D4×D29C2211yescharacteristic
18C2×D4×D29C2211yescharacteristic
19C29×#127C2211yescharacteristic
20C29×#125C2211yescharacteristic, complemented
21#11745300—21no—
22#11745300C2211yescharacteristic
23#11745300C2211yescharacteristic
24#11745299—21no—
25#11745299—21no—
26C2×#90783C2211yescharacteristic, complemented
27C2×#90783C2211yescharacteristic, complemented
28C2×#90773C2211yescharacteristic
29C2×#90772C2211yescharacteristic, complemented
30C2×C8×D29C2211yescharacteristic, complemented
31#11745260—21no—
32#11745259C2211yescharacteristic, complemented
33#11745259C2211yescharacteristic, complemented
34#11745256—21no—
35#11745254—21no—
36#11745254C2211yescharacteristic, complemented
37C4⋊C4×D29C2211yescharacteristic, complemented
38#11745252—21no—
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic
41C4×Dic58C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic, complemented
45C29×#102C2211yescharacteristic, complemented
46C29×#97C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48#11745180C2211yescharacteristic, complemented
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic, complemented
51#11745168C2211yescharacteristic, complemented
52#11745166C2211yescharacteristic, complemented
53#11745164C2211yescharacteristic, complemented
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4⋊#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C23×D29—21no—
61C2×D4×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69D4×D29—22no—
70D4×D29—22no—
71D4×D29—41no—
72D4×D29—41no—
73D4×D29—44no—
74C2×D116D411yescharacteristic
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29C2311yescharacteristic
79C2×C4×D29C2311yescharacteristic
80C2×Dic58C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90783—41no—
91#90783—41no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97#90781D411yescharacteristic
98C4⋊Dic29—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29D411yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105C4×Dic29—21no—
106C4×Dic29—21no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90773—22no—
110#90772—41no—
111C8×D29—41no—
112C23×C29—21no—
113C23×C29—21no—
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—81no—
120C22×D29—81no—
121C22×D29C2×D411yescharacteristic
122C22×D29C2×D411yescharacteristic
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—42no—
128D4×C29—81no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—42no—
135C22⋊D29—42no—
136C22⋊D29—42no—
137C22⋊D29—42no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29C2×D411yescharacteristic
142C2×Dic29C2×D411yescharacteristic
143D116—22no—
144D116—21no—
145D116#4112yes—
146C4×D29—21no—
147C4×D29—21no—
148C4×D29—21no—
149C4×D29—21no—
150C4×D29—42no—
151C4×D29—42no—
152Dic58—21no—
153Dic58—21no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3310—291nomaximal, Sylow
159C22×C29—41no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—21no—
167C2×D29—21no—
168C2×D29—21no—
169C2×D29—22no—
170C2×D29—21no—
171C2×D29—21no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—84no—
175C2×D29—84no—
176C2×D29AGL(1,ℤ/8)12yes—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29C2×#4111yescharacteristic
182C4×C29H(5,𝔽2)11yescharacteristic
183Dic29—21no—
184Dic29—21no—
185Dic29—41no—
186Dic29—41no—
187Dic29—41no—
188#552—291no—
189D42—291no—
190#490D2911yescharacteristic, complemented
191#482—291no—
192#480—291no—
193#478—291no—
194#468—291no—
195#465—291no—
196#460—291no—
197#450—291no—
198#450—291no—
199#440—291no—
200#435—291no—
201#418—291no—
202C2×#102—291no—
203C2×C29—81no—
204C2×C29—81no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—22no—
209D29—41no—
210D29—42no—
211C22×D4—291no—
212C22×D4—291no—
213C22×D4—581no—
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×M16—291no—
218C22×C8—291no—
219#127C2×D2911yescharacteristic
220#126—581no—
221#125—581no—
222#125C2×D2911yescharacteristic, complemented
223#123—581no—
224C22⋊Q8—291no—
225C22⋊Q8—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230#120—581no—
231C4×Q8—291no—
232C4×D4—291no—
233C4×D4—291no—
234#117—291no—
235#117—581no—
236C2×C4⋊C4—291no—
237#107—291no—
238#107—291no—
239#106—291no—
240C4⋊C8—291no—
241#103—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102C2×D2911yescharacteristic, complemented
248#102C2×D2911yescharacteristic, complemented
249#102C2×D2911yescharacteristic, complemented
250#102C2×D2911yescharacteristic, complemented
251C22⋊C8—291no—
252C22⋊C8—291no—
253#97C2×D2911yescharacteristic, complemented
254C29#331011yescharacteristic, complemented, Sylow
255C24—581no—
256C24—581no—
257C2×Q8—291no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—291no—
261C2×D4—291no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—582no—
265C2×D4—582no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—1161no—
269C2×D4—1161no—
270C2×D4—1164no—
271C2×D4C22×D2911yescharacteristic
272C2×D4C22×D2911yescharacteristic
273C22×C4—291no—
274C22×C4—291no—
275C22×C4—581no—
276C22×C4—581no—
277SD16—582no—
278SD16—1161no—
279SD16—1161no—
280M16—1161no—
281C2×C8—291no—
282C2×C8—291no—
283C2×C8—1161no—
284C2×C8C22×D2911yescharacteristic
285C2×C8C22×D2911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4C22×D2911yescharacteristic
296C4⋊C4C22×D2911yescharacteristic
297C22⋊C4—291no—
298C22⋊C4—291no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C42—581no—
306C42—581no—
307C42C22×D2911yescharacteristic
308C23—21no—
309C23—21no—
310C23—291no—
311C23—291no—
312C23—581no—
313C23—1162no—
314C23—1162no—
315C23—1162no—
316C23—1162no—
317C23—2321no—
318C23—2321no—
319Q8—581no—
320Q8—581no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—292no—
328D4—582no—
329D4—581no—
330D4—1162no—
331D4—1162no—
332D4—1162no—
333D4—1162no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—291no—
337C2×C4—291no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—581no—
345C2×C4—1162no—
346C2×C4—1162no—
347C2×C4D4×D2911yescharacteristic
348C2×C4D4×D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—581no—
353C8—581no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—292no—
361C22—581no—
362C22—581no—
363C22—581no—
364C22—582no—
365C22—581no—
366C22—581no—
367C22—1161no—
368C22—1161no—
369C22—2324no—
370C22—2324no—
371C22C2×D4×D2911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—581no—
377C4—581no—
378C4—1161no—
379C4—1161no—
380C4—1161no—
381C4#41×D2911yescharacteristic
382C4#1174536411yescharacteristic
383C2—81no—
384C2—81no—
385C2—582no—
386C2—1161no—
387C2—1162no—
388C2#1427180611yescharacteristic
389C2AGL(1,ℤ/8)×D2911yescharacteristic
390C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#490C2
socleC22×C29C22×D4
prime radical#14271798C2
hypercenter#490D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14271851C2semidirect
3. #14271485C2semidirect
4. #14271475C2semidirect
5. #14271460C2semidirect
6. #14271408C2semidirect
7. #14271391C2semidirect
8. #14271360C2semidirect
9. #14271315C2semidirect
10. #14271315C2semidirect
11. #14271265C2semidirect
12. #14271236C2semidirect
13. #14271166C2semidirect
14. #102×D29C2semidirect
15. C29×#490C2semidirect
20. C29×#125C22semidirect
26. C2×#90783C22semidirect
27. C2×#90783C22semidirect
29. C2×#90772C22semidirect
30. C2×C8×D29C22semidirect
32. #11745259C22semidirect
33. #11745259C22semidirect
36. #11745254C22semidirect
37. C4⋊C4×D29C22semidirect
41. C4×Dic58C22semidirect
42. C29×#102C22semidirect
43. C29×#102C22semidirect
44. C29×#102C22semidirect
45. C29×#102C22semidirect
46. C29×#97C22semidirect
47. #11745180C22semidirect
48. #11745180C22semidirect
50. #11745168C22semidirect
51. #11745168C22semidirect
52. #11745166C22semidirect
53. #11745164C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. C4⋊#6597C22semidirect
190. #490D29semidirect
222. #125C2×D29semidirect
247. #102C2×D29semidirect
248. #102C2×D29semidirect
249. #102C2×D29semidirect
250. #102C2×D29semidirect
253. #97C2×D29semidirect
254. C29#3310semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#142718512
#142717982
#142714852
#142714752
#142714602
#142714082
#142713912
#142713602
#142713152
#142712652
#142712362
#142711662
#102×D292
C29×#4902
#331029